基于二阶磁张量欧拉反褶积的磁源单点定位方法

Magnetic source single-point positioning based on second-order magnetic tensor Euler deconvolution

为了从强地磁背景场下有效分离小尺度磁性体的磁异常信息,提高磁源单点定位精度,本文提出了基于二阶张量欧拉反褶积的磁源单点定位方法。在平面十字形磁梯度张量系统基础上提出了二阶张量系统概念及测量方法,利用三维欧拉反褶积公式推导了磁异常场源一阶、二阶张量数据与位置矢量关系;在磁偶极子场源下推导了张量矩阵特征值的特征向量与磁源位置矢量间的衍生不变关系,并以此作为限定方程,据此解得磁源位置坐标。研究结果表明:仿真实验在均匀强磁背景环境下对单点目标进行了精确定位;实测数据经磁梯度张量系统误差校正后,对小尺度磁铁的定位精度控制在10cm均方根误差范围内。

In order to distinguish the magnetic anomaly of small-scale magnetic objects from strong geomagnetic field and improve the single-point positioning accuracy of magnetic objects,a single-point positioning method based on second-order magnetic tensor Euler deconvolution is proposed.First the concept of the second-order tensor system and its measurement are discussed based on the planar cross magnetic gradient tensor system.Then the relationship between first-order and second-order tensor data of magnetic source and their position vectors is derived with 3 DEuler deconvolution formula.Finally the invariant relationship between the eigenvectors of the tensor matrix eigenvalues and the position vector of magnetic source is derived under the magnetic dipole field,and magnetic source coordinates are calculated.Model data tests show that the proposed method can accurately locate single-point objects in a uniform strong magnetic field.Real data tests show that the proposed method achieves the small-scale magnet positioning root-mean-square error(RMSE)less than 10 cm after the system error correction.